Let S → A be a smooth family of surfaces whose general fibre is a smooth surface of P3 and whose special fibre has two smooth components, intersecting transversally along a smooth curve R. We consider the Universal Severi-Enriques variety V on S → A. The general fibre of V is the variety of curves on St in the linear system |OSt (n)| with k cusps and δ nodes as singularities. Our problem is to find all irreducible components of the special fibre of V . In this paper, we consider only the cases (k, δ) = (0, 1) and (k, δ) = (1, 0). In particular, we determine all singular curves on the special fibre of S which, counted with the right multiplicity, are a limit of 1-cuspidal curves on the general fibre of S.

Degenerating curves and surfaces: first results

GALATI, Concettina
2009-01-01

Abstract

Let S → A be a smooth family of surfaces whose general fibre is a smooth surface of P3 and whose special fibre has two smooth components, intersecting transversally along a smooth curve R. We consider the Universal Severi-Enriques variety V on S → A. The general fibre of V is the variety of curves on St in the linear system |OSt (n)| with k cusps and δ nodes as singularities. Our problem is to find all irreducible components of the special fibre of V . In this paper, we consider only the cases (k, δ) = (0, 1) and (k, δ) = (1, 0). In particular, we determine all singular curves on the special fibre of S which, counted with the right multiplicity, are a limit of 1-cuspidal curves on the general fibre of S.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11770/129440
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 7
  • ???jsp.display-item.citation.isi??? ND
social impact